biostats final exam

What does statistical distribution describe?

How values of a variable are spread across a population.

What does a Normal (Gaussian) distrubution mean/describe?

Bell-shaped, symmetric around the mean. Mean = Median = Mode.

Most parametric tests assume this shape. Approximate empirical rule: ~68% within ±1 SD, ~95% within ±2 SD, ~99.7% within ±3 SD

Example: blood pressure in healthy adults, serum cholesterol levels.

What does a right-skewed distrubution mean/describe?

Long tail to the right. Mean > Median.

Common for lab values that cannot be negative and are usually low.

Example: serum troponin, C-reactive protein, wait times.

What does a left-skewed distrubution mean/describe?

Long tail to the left. Mean < Median.

Example: age at death in developed countries (most people live to old age).

What does a uniform mean distrubution mean/describe?

All values equally likely across a range. Example: randomly assigned drug doses in a balanced trial design.

What does a bimodal distrubution mean?

Two peaks — often suggest two sub-populations.

Example: a pain score distribution mixing responders and non-responders.

What does the Central Limit Theorem (CLT) state?

Regardless of the shape of the original population distribution, the sampling distribution of the sample means will approach a normal distribution as sample size (n) increases — typically n ≥ 30 per group is sufficient.

What is randomization?

A process in clinical research that uses chance to assign participants to different study groups, ensuring that any observed difference in outcomes are likely due to the treatment rather than pre-existing difference between participants

What is Mitigating Bias when refering to randomization?

It prevents selection bias, where researchers might unitentionally assign healther paitents to a specific group, and accidentatl bias, which involves unforeseen imbalances in patient characteristics.

What is Statistical Validity when refering to randomization?

It provides a probabilistic basis for statistical tests. Models allow researchers to calculate p-values based on the actual prodcedure used, rather than relying solely on popoulation-level assumptions

What is Simple randomization?

Assigns participants based on a single sequence of random events, like a coin flip or computer-generated number

What is Block randomization?

Assignmetns are made in small “blocks” to ensure gorups remain balanced in size throughout the enrollment period

What is Stratified randomization?

Participants are first grouped by specific characteristics, then randomized within those goups to ensure balance for key prognostic factors

What is the impact of randomly assigning participants on known and unknown confounding variables?  

Randomization distributes known and unknown confounding variables equally across arms of the clinical study. In effect cancelling out confounding effects to reveal effect of the intervention.

What does p-value mean?

The probability of observing a result as extreme as - or more extreme than - the obtained, assuming the null hypothesis (Ho) is true.

Basically, how often would we see a difference this larger or larger by random chance alone?

What is the null hypothesis (H_o)?

The default assumption: no effect, no difference.

Example: "Drug A does not reduce LDL more than placebo."

What is the alternative hypothesis (H₁)?

The claim being tested: there IS an effect.

Example: "Drug A reduces LDL more than placebo."

What does an alpha (α) mean?

Pre-specified threshold. Usually 0.05. If p < α, reject H₀.

What does it mean when p < α?

Statistically significant. Reject H₀.

What does it mean when p ≥ α?

Fail to reject H₀. Insufficient evidence.

What does a Type I Error (False Positive, α) mean?

Rejecting H₀ when it’s actually true. It’s concluded that a treatment works when it does not, which leads to adoping an ineffective or harmful treatment, but this can be reduced by lowering α (but increasing β).

Equal to α (the significance threshold). At α = 0.05, there is a 5% chance of a Type I error in any single test.

What is an issue with lowering α?

Redues Type I errors but increases Type II errors

What does a Type II Error (False Negative, β) mean?

Failing to reject H₀ when it is actually false. You miss a real treatment effect, which leads to missing a beneficial treatment, but this can be reduce by increasing sample size/power.

Equal to β (typically set at 0.10-0.20). Statistical power = 1 − β.

What is a Confidence Interval (CI)?

A 95% CI is a range of plausible values for the true population parameter, calculated from sample data.

If the study were repeated 100 times, 95 of the resulting intervals would contain the true value.

How is CI used for difference in means?

Comparing a continuous outcome between two groups. The null value is 0.

How is CI used for Relative Risk?

When comparing the probability of a binary event between two groups. The null value is 1.0.

What does it mean when the Relative Risk is less than one (RR < 1)?

Treatment reduces risk (protective).

Example: RR = 0.72 → 28% relative risk reduction.

What does it mean when the Relative Risk is equal to 1 (RR = 1)?

No difference in risk between groups.

What does it mean when the Relative Risk is greater than 1 (RR > 1)?

Treatment increases risk (harmful).

Example: RR = 1.45 → 45% higher risk.

Why is the CI better than p-value?

It porovides MORE information and shows both significance AND the magnitude and direction of the effect.

A result can be statistically significant but have a CI entirely within a clinically trivial range.

What does it mean when something has statistical significance?

The observed result is unlikely to be due to chance (p < α).

This is a mathematical property determined by sample size, variability, and effect size.

What does it mean when something has clinical significance (pratical significance)?

The effect size is large enough to matter to patients and clinical practice.

This requires clinical judgment — no formula determines it.

What is Inclusion criteria?

A set of characteristics that the participants MUST have in order to be enrolled.

Example: adults aged 18- 65, diagnosed T2DM for ≥ 1 year, A1C 7.5-10%.

What is Exclusion criteria?

A set of characteristics that disqualify participation in the study.

Example: eGFR < 30 mL/min, current insulin use, pregnancy, history of pancreatitis.

What is the trade off for criteria?

Stricter criteria → Higher internal validity, lower external validity

Broader criteria → Lower internal validity, higher external validity

What is Internal validity?

The degree to which study results accurately reflect a true cause-and-effect relationship WITHIN the study sample.

It asks: "Can I trust this result for these patients?"

How does strict criteria INCREASE internal validity?

Excluding patients with comorbidities creates a homogenous population. This reduces confounding — competing variables that could explain the outcome. 

How does broader criteria REDUCE internal validity?

Including very heterogeneous patients introduces variability that can obscure the true drug effect, potentially diluting a real difference.

What is External validity (generalizability)?

The extent to which results apply to patients OUTSIDE the study.

It asks: "Do these results apply to my patient in the clinic?"

How does strict criteria DECREASE external validity?

If only a certain population were enrolled, findings may not apply to other populations.

How does strict criteria INCREASE external validity?

Pragmatic trials use broad criteria intentionally to maximize real-world appliciability

What is Statistical Power (1 − β)?

The probability that the study will correctly reject H₀ when H₁ is true — i.e., detect a real treatment effect when one truly exists.

Usually Power ≥ 80% (β ≤ 0.20) is the minimum acceptable for most clinical trials. High-stakes trials may require 90% power.

What criteria must be changed to INCREASE power?

Sample size ↑

Effect size ↑

α ↑

Variability ↓

What criteria must be changed to DECREASE power?

Sample size ↓

Effect size ↓

α ↓

Variability ↑

What does an assumption on Normaily mean for a paramertric test?

The data follow a normal distribution. Critical becasue parametric tests use the mean and standard deviation in their calculations.

If violated, the p-values and CIs may be inaccurate - false positives or false negative may result - use non parmetric alternatives.

What does an assumption on Homogeneity of Variance (Homoscedasticity) mean for a paramertric test?

Variance of the outcome is approximately equal across all groups being compared. Especially important for ANOVA and independent t-test

If violated, the Type I error rate inflates - more false positives than expected at the chosen α - use tests that adjust for unequal variances

What does an assumption on Independence of Observations mean for a paramertric test?

Each data point must be independent - one observation must not influence another.

What does Repeated Measures mean?

Pre/post measurements on the same patient are NOT independent → use paired t-test or repeated-measures ANOVA.

What does Clustered Data mean?

Patients from the same clinic tend to be more similar to each other than to patients from other clinics → use mixed-effects models.

What do Family Studies mean?

Genetic data from siblings are correlated → standard independence assumption is violated.

What does an assumption on Inteval or Ratio scale data (Continuous data) mean for a paramertric test?

Data must have meaningful numeric differences. Parametric tests require that arithmetic operations (mean, SD) are interpretable

What is a Nominal scale?

Categories with no order. Does not support Mean/SD.

Example: Sex, Drug class, Blood type, Alive/Dead

What is an Ordinal scale?

Ordered categories but intervals are NOT equal. Does not support Mean/SD (median preferred)

Example: Pain: mild/mod/severe; NYHA class 1–4

What is an Interval scale?

Equal intervals but no true zero. Supports Mean/SD.

Example: Temperature in °C — 0°C does not mean "no temperature."

What is a Ratio scale?

Equal intervals AND a true zero. Supports Mean/SD.

Example: Blood pressure (mmHg), serum creatinine (mg/dL), age (years), drug dose (mg).

What is an independent t-test?

Compare MEANS of a continuous outcome between TWO INDEPENDENT groups (different subjects in each) with key outputs being t-statistic, degrees of freedom, p0-value, 95% CI for difference in means.

Allows for normality in each group; homosecedasticity; independence; interval/ratio scale.

H_o: Mean group 1 = Mean group 2 (difference = 0)

What is a paired t-test?

Compares MEANS within the SAME SUBJECTS at two time points or conditions which allows for controls for between-subject variability - more powerful than independent t-test for paired data.

Used in pre/post treatment in the same patients; matched pairs; crossover designs

H_o: Mean DIFFERENCE between paired observations = 0

What is an One-Way ANOVA test?

Compares MEANS across THREE OR MORE independent groups simultaneously. It maintains overall α.

H_o: All groups means are equal (μ₁ = μ₂ = μ₃)

What is a Simple Linear Regression?

Quantify the LINEAR relationship between ONE continuous predictor (X) and ONE continuous outcome (Y)

H₀: β₁ = 0 (no linear relationship between X and Y)

What is a Logistic Regression?

Model the relationship between predictors and a BINARY outcome (yes/no, event/no event).

The output of odds ratios with 95% CI for each predictor. CI must exclude 1.0 for statistical significance.

H₀: OR = 1.0 (predictor does not affect the odds of the outcome)

What does an Odds Ratio greater than 1 (OR > 1) mean?

Increased odds of outcome

What does an Odds Ratio less than one (OR < 1) mean?

Decreased odds of outcome

What is a Multiple (Multicariate) Regression?

Assess the independent contrubution of MULTIPLE predictors on one outcome simultaneously, controlling for confounding. Each β or OR represents the effect of that predictor holding ALL other predictors constant.

What is a Tests of Difference (Two-Sided Hypothesis Test)?

Determines whether a new treatment produces a DIFFERENT outcome from the comparator - in either direction. Most common trial design. A Two-tailed (non-directional) - rejects H_o if difference is extreme in either direction. Requires p < α/2 in each tail for a two-tailed test.

H_o: New = Standard (no difference)

H₁: New ≠ Standard (could be better OR worse)

95% CI for difference that EXCLUDES zero → statistically significant

What is an Equivalence Trials (TOST - Two One-Sided Tests)?

Demonstrates that a new treatment is EQUIVALENT to the standard - neither meaningfully better nor worse. Used for generic drug approval and biosimilar comparisons.

H_o: |New − Standard| > Δ (the treatments are NOT equivalent — they differ by more than the margin)

H₁: |New − Standard| ≤ Δ (the treatments ARE equivalent — difference is within the margin)

The ENTIRE 95% CI must fall within ±Δ to conclude equivalence

What is a Superiority Trial?

Demonstrates that a new treatment is BETTER than the coparator by a clinically meaningful amount. Distinguished from a test of diffrence by prespecifiying that the nrew treatment must exceed the standard by more than a trivial margin.

H_o: New ≤ Standard (new is not better)

H₁: New > Standard (new is better by more than a trivial amount)

95% CI for difference is entirely on the beneficial side (excludes null) → superiority shown. If CI crosses null → superiority NOT demonstrated.

What is a Non-inferiority Trial?

Demonstrates that a new treatment is NOT MEANINGFULLY WORSE than the standard. The new treatment may offer advantages even without superior efficacy but there must be a pre-specified threshold of acceptable inferiority.

H_o: New is inferior by more than −Δ (lower CI bound is below −Δ)

H₁: New is non-inferior — lower CI bound is above −Δ

Lower bound of 95% CI must be above −Δ to conclude non-inferiority. Requires checking CI bound, not just point of estimate.